Biological membranes serving as envelops of cells and cellular organelles adopt highly intricate shapes.  A common architectural feature of these organelles is a huge excess of the surface area compared to that minimally needed to covers the internal volume, which must be related to the organelle functions requiring an efficient molecular exchange between the internal volume and the surrounding cytosol. This geometrical property is achieved by strong deviations of the organelle shapes from the spherical ones, which can be realized by a, practically, infinite variety of membrane configurations. Particular intricate shapes referred to as superstructures are achieved by membranes of such intracellular organelles as endoplasmic reticulum (ER), Golgi Complex, mitochondria and protrusions of the plasma membrane. Membrane superstructures are generated through mechanical interplay between the lipid bilayer membrane matrix and the membrane associated proteins. The goal of the talk is to overview our recent progress in understanding the physics behind formation of membrane superstructures in three particular systems: stacks of ER sheets; Lipid Droplets; and clusters of caveolae on plasma membranes. After a short introduction into the continuous elasticity model of membranes I will present computational results on the “parking garage” configurations of ER stacks, conformations of ER tubules containing Lipid Droplets, and rosette-like assemblies of caveolae. Unresolved problems related to the considered systems will be mentioned.